Mobile Information Systems

Volume 2016 (2016), Article ID 2152538, 11 pages

http://dx.doi.org/10.1155/2016/2152538

## Rank-Constrained Beamforming for MIMO Cognitive Interference Channel

College of Information Science and Technology, Jinan University, Guangzhou 510632, China

Received 29 January 2016; Revised 14 April 2016; Accepted 5 May 2016

Academic Editor: Yunfei Chen

Copyright © 2016 Duoying Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper considers the spectrum sharing multiple-input multiple-output (MIMO) cognitive interference channel, in which multiple primary users (PUs) coexist with multiple secondary users (SUs). Interference alignment (IA) approach is introduced that guarantees that secondary users access the licensed spectrum without causing harmful interference to the PUs. A rank-constrained beamforming design is proposed where the rank of the interferences and the desired signals is concerned. The standard interferences metric for the primary link, that is,* interference temperature*, is investigated and redesigned. The work provides a further improvement that optimizes the dimension of the interferences in the cognitive interference channel, instead of the power of the interference leakage. Due to the nonconvexity of the rank, the developed optimization problems are further approximated as convex form and are solved via choosing the transmitter precoder and receiver subspace iteratively. Numerical results show that the proposed designs can improve the achievable degree of freedom (DoF) of the primary links and provide the considerable sum rate for both secondary and primary transmissions under the rank constraints.

#### 1. Introduction

Cognitive radio (CR) network is a potential solution to enhance spectrum utilization by allowing coexistence with licensed networks. The concurrent transmissions are allowed in the spectrum sharing cognitive radio networks by keeping the CR interferences to the primary user receivers (PU-Rxs) under an acceptable level. Hence, an effective approach to control the interference level is of critical importance to underlay CR networks.

Recently, interference alignment (IA) has been developed to achieve the maximum spatial degrees of freedom in the user interference channel, which guarantees an interference-free received signal by forcing interferences into a reduced-dimensional receiver subspace [1–13]. Considering its potential to mitigate the interference, the IA is widely introduced to multiple-input multiple-output (MIMO) cognitive radio system [14–19], MIMO relay system [20], multihop MIMO networks [21], and the simultaneous wireless information and power transfer (SWIPT) system [22]. In the MIMO CR networks, the upper bound and lower bound of achievable degrees of freedom (DoF) have been studied with global channel information [1, 23], and the CR interferences to the PUs are nulled in [14–16]. However, the global channel state information usually is not available, which may lead to severe CR interferences to PU. As a result, the practical algorithm is developed that minimizes the interference leakage power by selecting the precoding and receiving beamforming matrices alternatively [16, 23–25]. In [16], the active IA and success interference cancelation (SIC) techniques are combined to transmit data over MIMO underlay CR network. Moreover, an efficient antenna selection IA algorithm based on discrete stochastic optimization (DSO) is proposed to improve the received signal-to-interference-and-noise ratio (SINR) of each user in IA-based CR networks with low complexity [17]. In the abovementioned works, the interference temperature is considered as a standard interference* metric* that suppresses the CR interferences and guarantees the quality of service (QoS) of the primary transmission. Considering the available eigenmodes distributed among the SUs and PUs, the adaptive number of eigenmodes beamforming (ANEB) algorithm for the PU is developed which adjusts the number of PU’s eigenmodes to meet its rate requirement [26]. It suggests that the DoF of the receiving eigenspace is of crucial importance to the system performance, which motivates us to revise the standard interference* metric*, that is, interference temperature, in the underlay CR networks.

In this paper, the rank-constrained beamforming design is developed for underlay MIMO CR network. Instead of using the standard interference metric,* interference temperature*, the CR interferences to the PU-Rxs are controlled by a rank constraint that aligns the CR interferences into a reduced-dimensional subspace. As a result, the CR interferences are suppressed in a low-dimensional subspace, rather than an acceptable low level of the received power; consequently the achievable DoF of the intended primary signal is guaranteed. The optimal transmit precoding and receiving beamforming are selected by minimizing the total interference of the secondary transmission subject to the rank constraint on the CR interferences. Different from those designs based on Cadambe-Jafar scheme [14–16], the proposed design strives to null the CR interferences at the PU-Rxs without the global channel state information. Considering the benefits of the multiplexing gain/DoF, we further maximize the achievable DoF of the secondary links by minimizing the dimension of the interferences of the secondary transmission while maintaining the full rank of the desired signal matrix and the low rank of the CR interferences to PUs. Due to the nonconvexity of the rank, the proposed optimization problem can be approximated as convex form and efficiently solved via alternating minimization. Simulation results show that the proposed scheme can improve the sum rate of both PU and SUs due to the effective rank constraint on the CR interferences.

This paper is organized as follows. The system model is introduced in Section 2. Section 3 presents the rank-constrained interference minimization algorithm, followed by further improvement in Section 4. Simulation results are presented and discussed in Section 5. Concluding remarks are given in Section 6.

*Notations*. Matrices and vectors are type-faced using slanted bold uppercase and lowercase letters, respectively. Conjugate transpose of the matrix is denoted as . Positive semidefiniteness of the matrix is depicted using , and is an identity matrix with the dimension equal to . is used to describe the complex space of matrices, and denotes a complex Gaussian distribution with mean and covariance . Finally, mathematical expectation is described as . The trace, nuclear norm, and Frobenius norm of a matrix/vector are denoted by , , and , respectively.

#### 2. System Model

Consider a MIMO cognitive radio network with PU and SUs, shown in Figure 1. The secondary transmitter (SU-Tx) is equipped with transmit antennas and receiving antennas at the th SU. The transmission of all users is synchronized such that each simultaneously begins and ends each transmission, and no frequency or timing offsets exist in the network [2, 6]. In the primary links, there are transmit antennas and receiving antennas equipped at each PU. Without any loss of generality, we assume that the users are indexed so that users are SUs and the users are the PUs. The total signal received at the th secondary user receiver (SU-Rx) can be expressed aswhere represents the transmitted signal from the th SU-Tx with equally loaded power and denote the flat-fading channel from the th SU-Tx to the th SU-Rx receiver. The columns of the precoding matrix are orthonormal basis of the th transmitted signal where (for all ), and the receiver thermal noise is assumed as the complex additive white Gaussian noise with covariance ; that is, . Note that any interference from the PU-Tx is assumed to be neglected. (This can be possible if the PU-Tx is located far away from the secondary users, or the interference is represented by the noise under an assumption that the PU-Tx’s signal is generated by random Gaussian codebooks [27]. In IEEE 802:22 standard, the secondary wireless regional area network (WRAN) is located far away from the primary TV transmitter and hence the interference from the primary TV transmitter can be neglected at the receiver.) Similarly, the received signal at the th PU-Rx can be expressed aswhere represents the transmitted signal from the th PU-Tx with equally loaded power, denote the channel from the th PU-Tx to the th PU-Rx, and is the channel from the th SU-Tx to the th PU-Rx. The columns of the precoding matrix are orthonormal basis of the transmitted signal from the th PU-Tx, and the receiver thermal noise is assumed as the complex additive white Gaussian noise with covariance ; that is, . Note that the first term in (2) is the received intended signal of the th primary link, the second term is the interferences from other primary links, and the third term is the CR interferences to the corresponding PU-Rx.